Enticing Students to Think with Food

What better way to end our semester than a few tasks involving food?  Sometimes the last weeks of school can be filled with multiple distractractions.  In hopes of holding my students’ attention while they’re in class, I am bribing them to think with food.  Yes, I have fallen to enticing them with external rewards.

 

 

 

 

With the Oreo Mega Stuff,  A Recursive Process offers some research by Chris & Chris.  My plan is to follow the QFT model outlined here.  I just recently became aware of the Question Formulation Technique which I shared in this post.  The Q-Focus is simply to display my package of Mega Stuf Oreos, wondering what questions they have – recording all of their comments as questions …and follow the process allowing them to determine their own questions, lead their own learning.  Though I would hope they would approach this from a volume stand-point – letting them design their own questions may lead to other ideas and I am fine, so long as they are thinking and talking math, yes they may eat their research tools once they’ve answered their chosen question.  The final product will be a 30-second pro/con commercial Mega vs. Original supported by their mathematical findings.

Offering several stations to review surface area and volume formulas utilizing various candies as they are packaged as well as the infamous pouring water from a pyramid to a cube / cylinder to a cone will be modeled as one of the station activities.

Finally, using the  Ice Cream Cone  found at Illustrative Mathematics.

ICE CREAM prompt and file

As a “reward” for successfully completing this task, I think a class Ice Cream Party would be appropriate.  I just need to know how much ice cream I should purchase to ensure everyone has plenty to enjoy without too many leftovers.  Assuming the cones are filled with ice cream with a “spherical” scoop atop – sounds like a great homework practice problem to me…

Geometric Measurement and Dimension (GMD)  Explain volume formulas and use them to solve problems

• G-GMD.1 – Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
• G-GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.^★
• G-MG.A.3 : Modeling with Geometry- Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Several times this year, I’vfe gotten the GMD (geometric measureme and dimension) and MG (modeling with geometry)domains mixed up, I am slowly beginning to internalize the new notations.

I also like this prompt: Doctor’s Appointment for GMD-A.3.

On a side note – Reading an article in MT the other night – I wondered, “Was I supposed to know that?”

The derivative of area of a circle is the circumference?  The derivative of volume of a sphere is surface area?  Similarly…derivative of area of square is half the perimeter, derivative of volume of cube is half surface area…  How/Why did I miss that? Or did I know it at some point but just pushed it aside years ago?  Interesting…made me wonder and I started looking at other figures – will share more later.

Trig Ratios – #made4math

Through the years, I’ve seen students struggling trying to remember which Trig Ratio is which.  I have a colleague who draws a big bucket with a toe dipped into the water.  She says she tells the students “Soak-a-Toe” to help them recall SOH-CAH-TOA.  Another has described the “Native American”  SOH-CAH-TOA tribe as the one who constructs their teepees using Right Triangles.  The most entertaining though is the rap from WCHS Math Department “Gettin’ Triggy Wit It” on youtube.

I wanted to use an inquiry activity to help them develop the definitions of the Trig Ratios.  Basically, they constructed 4 similar triangles, found the side measures, then recorded ratios of specific side lengths.  Next, I had them measure the acute angles, then we used the calculator to evaluate the sin, cos and tan for each angle measure.  Students were asked to compare each value to the ratios they had recorded in the table and determine which ratio was closest to their value.  Here’s the file Similar Triangles Trig Ratios.  Anyway, its not a perfect lesson, but a starting point.  If you use it, please comment to let me know how you modified it to make it a better learning experience for estudents.

In the past, students sometimes struggle trying to decide which ratio they need to use when solving a problem. I put together an activity adapted from a strategy called  Mix-Pair-Freeze I’ve used from my Kagan – Cooperative Learning and Geometry book.  This book offers numerous, quality activities for engaging your students.

You can make copies of this file, Trig Ratio Cards File, then cut cards apart to use.

Each student gets a card.  They figure out which Trig Ratio is illustrated on their card (& why).  They mix around the room (with some fun music would make it better), then pair up with someone.  Each person tells which Trig Ratio and why (can be peer assessment, if one is mistaken).  They swap cards, mix and pair with another classmate.  This continues for several minutes, allowing students to pair with several different people.

When I call “Freeze!” Students are to go to a corner of the room which is designated Sin, Cos or Tan.  Within the group in each corner, students double check one-another’s card to determine if they are at the right location.  Again, peer assessment, if someone is wrong, they coach to explain why, then help them determine where they belong.

Students swap cards, mix-pair-freeze again.

I like this activity for several reasons:

• 1. Students are out of their seats and active.
• 2.  Students are talking about math.
• 3.  It allows them to both self-peer assess in a low-stress situation.
• 4.  I can listen to their descriptions and address any misconceptions as a whole-class as a follow-up.

 

To clarify, the intent of this activity is for students to determine what information they are given in relation to a given angle, then decide which ratio it illustrates. It is meant to help students who struggle deciphering what information is given.

Questions, Blocks & Shadows…

What a chain of events.  Last summer I created Pinterest boards to tag some amazing classroom ideas I kept running across.

This post, Blocks and Shadows from Best Case Scenario intriqued me. 

Several weeks ago, I was reading some posts by@jgough at Experiments in Learning by Doing where she suggested the book Make Just One Change, Rothstein & Santana (2011) .  The premise is to help student ask their own questions.  This book was deinitely on my summer reading list.

A few days ago, I mentioned the same book to @druinok on Twitter, which leads one of the book’s authors to my blog.  He shares a link to The Right Question.  Last night, I take some time to check it out and read an article Teaching Students to Ask Their Own Questions which briefly outlines 6 steps of the QFT -Question Formulation Technique.

So where is this going?  After working yesterday to complete a narrative for an application I’m submitting this week, my mind is in a mode where it won’t shut down.  I woke at 5 this morning, thinking about blocks, shadows, QFT.

Here are my thoughts…

1. I share pictures from our opening discussion of our Right Triangle Similarity unit, which include snapshots from The Vietnam Veteran’s Memorial in Frankfort, Kentucky

 From the memorial website: The design concept is in the form of a large sundial. The stainless steel gnomon casts its shadow upon a granite plaza. There are 1,103 names of Kentuckians on the memorial, including 23 missing in action. Each name is engraved into the plaza, and placed so that the tip of the shadow touches his name on the anniversary of his death, thus giving each fallen veteran a personal Memorial Day.

The location of each name is fixed mathematically by the date of casualty, the geographic location of the memorial, the height of the gnomon and the physics of solar movement. The stones were then designed and cut to avoid dividing any individual name.

and other shadow snapshots of random objects outside my classroom.

 

I am hoping this will be enough for my Q-focus, but since I have not read the book, I feel like there’s more to it.  Improvements to the lesson next time…

Next, set out blocks, flashlights, making available measuring tools such as grid paper, rulers, protractors, etc.

2. Students get time to play, explore and prodcuce questions!

Prior to beginning 2, I will explain certain steps and “rules” from the QFT model outlined here.

The 4 rules as discussed in the article: ask as many questions as you can; do not stop to discuss, judge, or answer any of the questions; write down every question exactly as it was stated; and change any statements into questions.

Here is where I need some help, I feel like I should impose a time limit to keep students focused and on task, but what is reasonable?  Even with an imposed time limit, I am one who will bend if I see my students are on task and into the mathematical discussion.  My initial thoughts are 10-20 minutes to explore and generate their questions before moving to the next step.

3.  Students improve their questions, noting difference between closed/open, etc.
4. Student prioritize questions, submit their focus to the teacher.
5. Discuss next steps.
6.  When all is said and done…reflection on their learning.

Please offer suggestions or even how you’ve used a similar activity in your classroom.  I am VERY interested in offering more lessons like this – where students guide their own learning.

Evaluating Statements About Length and Area

This lesson can be found http://www.map.mathshell.org same as title of the post.

This is one of six cards students discussed within small groups today. A student stated, “this is going to be a thinking day,” as they began removing the clips to start reviewing their cards. Most students would quickly come up with an always, sometimes or never true. However, to create their own examples or counterexamples to either justify or refute the statements was a struggle for some of them. Several groups had similar statements for this particular card. It was when a student asked, “do they have to be triangles?” that a turning point came for some.

Within our share out as a whole group, a student shared examples of reducing area, same perimeter and less perimeter. A question they wondered…can you reduce the area but increase the perimeter?

I really enjoy days like this, students are giving me the information, I am their scribe and I am slowly learning to let them determine if they agree or disagree with each others’ claims. I’m not even sure where the key is, that way I am actively having to listen to their arguments to determine if I agree or not. (Shout out to Max @Math Forum, I am listening to my students, not listening for the answer!) I go through the cards myself prior to the day of the lesson, just like I require them to do. But I am still closed minded in my own thinking at times. Why would you limit the example above to only triangles? Because that is what shape was presented on the card. However, does it state triangles only? Nope.

A task like this may drive some teachers crazy. Once you start considering different shapes, you begin to see what works for one, may not work for another. I had students cutting scrap paper, tracing patty paper, measuring side lengths…without me telling them to do it.

The classic question, a square and circle have equal perimeters, which has the larger area? I will do my best to share more reflections as we wind up tomorrow, if we wind up tomorrow…depending on their questions, discussions, claims and supporting evidence.

Quadrilateral Diagonals Properties

Over spring break, I was surfing online resources, searching for ideas and suggestions on how to plan and be more purposeful with the Mathematical Standards, which I have realized this year just how key these are to the success of CCSS. As I looked through Inside Mathematics , I ran across some PD training materials. I watched clips from Cathy Humphrey’s class. The Kite Task, an investigation of quadrilateral properties from seemed like a great activity to ease back on day 1 when we returned.

The task in short is for a kite company, who wishes to launch a new line of kites consisting of all types of qudrilaterals. The students are asked to devise a plan for how to cut/assemble the braces for each type of kite. They are only working with the diagonals in the investigation.

Rather than running copies and cutting out, I used my paper cutter to cut 1″ strips one color card-stock lengthwise and 1″strips width wise of a different collor (I didn’t realize how helpful this would be until later on). I created a strip to use as a guide on each strip, placed 7 holes equally spaced. Odd amount is best since they will be looking at bisectors some.

Each student would receive 2 of one color and 1 of another color.

Here are some snapshots of possible braces built.

For anyone who is having trouble visualizing, I’ve added some “sides” to the diagonals:

As we began the 2nd day of class, a few groups needed just a bit more time to wrap up their investigation. Using fist to five, I asked how many they still needed to determine. Most groups only 2 or 3, so I set the timer to keep us on track. I love days like this to walk around and just listen.

As I was questioning one of the groups, trying to ensure an absent student was on track, I asked the group’s members to “fill an order” – pick 2 sticks and construct the diagonals needed to brace…kite that was a rhombus, then another shape, etc to quiz them for understanding. AHA! Why couldn’t I use this as a formative assessment for the entire class?!?! Perfect.

When all groups had completed and debriefed a bit, I placed orders for kites and the students had to build the braces and pop up to show me for a quick assessment.

These pics were actually a geometrically defined kite. If you look closely, you can see a few wrong repsonses. To address these, I used extra sets of sticks to build a correct example and an incorrect example. To ask for suggestions why one was and the other was not correct. Why was one example actually a rhombus, allowing them to really compare/contrast the two figures.

Another great mistake I saw…when asked to create a rectangle, the top sketch is what I saw from about 6 students. Of course, my initial thought was, they dont understand the diagonals must be congruent.

Then I saw a student trace their shape in the air…second sketch. I literally saw their thinking. They had not used the sticks as diagonals. Clarified and corrected!

A post-it note quiz today, I built the braces, they had to tell me the quadrilateral name. A stop-light self assess, revealed most were confident, of the 10 yellows, 7 got all parts correct. The others missed 1, 2 or 3. All green students had each part correct.

We did a little speed dating to use properties to solve problems. As I listened to their approaches, most everyone seemed on track. Overall, I was very pleased with the results of the lesson.

Chalk Talk part 2 #makthinkvis

Another task I presented students in the form of a Chalk Talk…

We had previously used a patty paper lesson to construct our kites.

Simply enough, we constructed the kite by first creating an obtuse angle, with different side lengths. Folding along AC, tracing original obtuse angle using a straightedge to form the kite. Immediately students made comments about the line of symmetry. They were given time to investigate side lengths, angles, diagonals, etc. forming ideas and testing them to prove properties.

Their Chalk Talk task was to devise a plan to calculate the area of a kite.

Most every group approached the problem by dissecting the kite into right triangles, then combining areas. Several approached dissection as top triangle/bottom triangle, but would have to adjust their thinking when I asked them test their idea with specific total diagonal lengths. Some even extended the kite to create a rectangle. In the end, our discussion centered around 3 statements/procedures for finding area of a kite.

1/2(d1*d2) (d1*d2)/2 d1*d2

Allow them to determine which will /will not work and share evidence as to their conclusions. (Hello! MP3 critique reasoning of others.)

Sure, it would have been quicker to say here’s the formula, here’s a worksheet, practice, learn it. But its so much more fun “listening” to their Chalk Talk. Again, the end discussion is key-allowing them to think / work through each group’s findings, address any misconceptions and finally coming to a concensus as a class.

Chalk Talk part 1 #makthinkvis

I have wanted to try Chalk Talk, a strategy from our #makthinkvis bookchat, for several weeks.  However, I wanted it to be an authentic learning experience rather than a contrived activity just to say we did it.  This past 2 weeks, I found myself able to use it in 2 very different contexts.  Chalk Talk requires students to communicate written dialogue, no verbal.

The first was at the end of a unit of study.  I used the “2 Minute Assessment Grid” discussed here,

as a reflection tool for my students a couple of days before the unit assessment.  At the end of the previous post, I wondered how to address student questions/misconceptions.  I chose to recopy the questions onto a post it, placed in the middle of a dry erase poster.  Students were curious as they entered the room that afternoon and saw the posters hanging around.

Students took a dry erase marker and were instructed to respond without verbally talking, to suggest, explain, give examples or ask questions on the posters. 

Notice 2 posters were red.  I explained to students that red flags went up for me as I read the statements from their classmates post-it note reflection on the 2MAG. 

After students had opportunities to respond on each poster, we carouselled around to read responses.  I’ll be honest, I was hoping for more guidance, in depth statements from them.  There were some good examples, but majority were point-blank, straight forward surface statements without in depth explanations.  However, as we discussed the posters, I felt the thoughtful ideas came through.  “Here’s how I remember this…”, “If you can think of it this way…”

Which shows most of them can verbally give ideas, explanations but written is not as strong.  How do we assess them? High stakes testing is almost always written.  Another reason I am not am not a fan.  It just seems unfair we judge students and even teachers based on written, mc tests that don’t allow opportunity to showcase strengths of all students.

Overall, I feel like this task gave students a chance to address those ideas they were still fuzzy on, gaining suggestions from classmates, whether written in the Chalk Talk or our wrap up discussion.  On our unit assessment, questions that targeted the concepts from Chalk Talk, students performed very well on.  I do feel the opportunity to discuss/process verbally as the follow-up is key. A wrap upmdiscussion gave me opportunity to address any unclear / incorrect comments as well.

I look forward to finding more opportunities to use Chalk Talk to move learning forward and make thinking visible.

Triangle Centers #made4math Monday

I stumbled upon a learning task this weekend on a Georgia DOE site involving triangle centers.  The task is simply to choose a location for an amusement located between 2 cities.  Yep. Simple enough, until I sat down and started deciding how I would approach the situation. 

The final task is for students to write a memo with their recommendation when cost of building new roads is taken in to account. 

Here is a copy of the task Triangle Centers Amusement Park

I am looking forward to reading what recommendations my students give and their reasons why!

Providing Students Time to Reflect #makthinkvis

Making Thinking Visible online chat has really challenged me to think differently this semester about my questioning, looking for opportunities for students to share their ideas but most importantly, giving them time to reflect.

To begin our unit on triangles, I used the Generate-Sort-Connect-Elaborate, with plans to elaborate towards the end of the unit. As a class, I simply went around the room, each student generating an idea/concept related to triangles and I added what they shared to the list.  I placed students in groups of 3 and asked them to sort the ideas any way they wanted and to connect each set of ideas to the triangle central theme.

Most had measuring, classifying/types, etc. However, several had made some connections back to our Day 1 activity with the Chaos game, Sierpinksi’s Triangle, Midsegments and their properties.

Today, in class, I asked them to flip back to INB page 47 and take a couple of minutes to do nothing but read through their original concept maps/webs. Before I could give them further instructions, one asked if they could add to it? Of course! That’s exactly what I want you to do! I’ll see if I can manage some before/after pics.  The following few minutes were great. Listening to them think and share outloud. One even said, “Man, I’ve sure learned a lot!”

The next task is one I read about inmy reader a few weeks ago. I apologize, if you blogged about this and I’ve forgotten your name, but I really, really liked it! I gave each student 4 sticky notes, directing them to place a + sign in the corner of one, ? on another, ! on the third and finally a student asked, “you’re not going to make me draw a lightbulb are you?!?”

I explained what each note would include:

+ One Improvement – this could be either an improvement they still needed to make OR an improvement I could make in teaching the unit. A student asked if it could be something they improved on during the unit..sure!

! What NOT to forget!

? A question they still have.

Lightbulb moment during the unit…

I gave them some time to flip back through their INBs, instructed them to place their notes on the board in the back of the room.  A few asked if they could bring theirs in tomorrow. 

A quick glance showed that many still are not comfortable with proofs, a few are having trouble with the ‘names’ of triangle centers. I am more concerend they know/understand each of the centers’ special properties for problem solving. There were a variety of lightbulb moments.  And even a few misconceptions are obvious in some of their responses.

My plan is to address common questions as whole class.  I had originally thought I would respond to the individual questions/misconceptions by using different color sticky notes up on the board.  However, now, I’m thinking I may recopy some of the misconceptions onto dry erase boards and use them in a chalk talk carousel activity. 

To begin, have a variety of comments, some I agree with and others I am concerned with.  Give students red, yellow, green stickers – they carousel through the statements, placing green on those they agree with, yellow or red on those they have questions about.  Would this or the chalk talk be more beneificial here? 

Environment for Thinking Part 2 – Step Inside Room 123 #makthinkvis

If you knew nothing about me, but you walked in my classroom – I wonder…

What you would see?  What would you notice?
What do you think is going on?
What does it make you wonder? What questions do you want to ask?

What does it say about about me as a teacher, about the learning opportunities I provide my students?

As you walk in to Room 123:

Standing at the back, looking to the front:

Standing by exterior wall:

Front looking to back:

From a couple of weeks ago…triangle congruencies:

Question from student led to this sketch…original question stated shortest distance from B to AC was 5 in., how many places could D be located so BD would be 6 inches. Student asked would angle b ever be right angle? Another question, how long would AD have to be in order for angle B to be obtuse?

I’ll be honest, as I stood in the middle of my room, looking around, I was disappointed. On this particular day, there was little evidence of student learning/thinking. There’s not a lot of wall space in the square 23×23 ft. room.

Where? How? What types of evidence of student thinking and learning do you have up in your room?

The idea was not to necessarily to display student products, but learning tasks, chalk talks, documentation of discussions, concept maps that is left up for students to view/have access to during a unit of study. I welcome ideas, suggestions of ways I could improve…